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(2)

: log - ln vv! ( v .)

35

, - ex+y = ex ey .

a = ex, b = ey . = ln(a), y = ln(b) . x + y = ln(a) + ln(b) = ln(ab). ex+y = ab = ex ey v .

e - .

a > 0 v - = exln(a) .

36

> 0 (ab)c = abc, x+y = ax ay .

.

1 = 1 . > 1 v , < 1 v . axlog(a), logax ln(x)/ln(a) .

f(x) = g(x)h(x) .

g(x)h(x) = eh(x)ln(g(x))

. 8-

v, v vv 8- .

v f(x)=xa v v. v - .

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f(x) = xa (x) = axa-1

f(x) = xa = ealn(x) .

v. ex vv .

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n - .

.

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n = 0 v . ex > x vvv . - vv . ln - x > ln(x) > 0 v . < 1 v ln(x) . > 1 v :

x - 1 f(t) = 1/t [1, x] S . ln(x) < x - 1 < 1.

.

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1 - ( ex > x), .

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. 1 - , --> . 1/(nn) v .

(1) | vv | -->


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